How do you multiply and simplify $(sinx+cscx)(sin^2x+csc^2x-1)$ ?

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Answer 1 · 2016-10-12T10:46:12

$(sinx+cscx)(sin^2x+csc^2x-1)=sin^3x+csc^3x$

Recall the identity

$(a+b)(a^2+b^2-ab)=a^3+b^3$

As $sinx xx cscx =1$ , we can write

$(sinx+cscx)(sin^2x+csc^2x-1)$ as

$(sinx+cscx)(sin^2x+csc^2x-sinx cscx)$

= $sin^3x+csc^3x$

How do you multiply and simplify (sinx+cscx)(sin^2x+csc^2x-1)(sinx+cscx)(sin^2x+csc^2x-1)?